Just so you know, we do live and work in London. We joined the Tate Museums and I went to see the Dali exhibit three times before it left so I could sit through all the films. Before the days got really really short, strolling the Thames from St. George's Wharf to the Tate and back was an almost daily event.
I also really enjoy hitting Borough Market on Fridays. Though it pains me to say it, it really does outshine Eastern Market by leaps and bounds. From the guy who only sells Parmesean Reggiano to the olive people, the various bread folks and of course the truffle guy, it's an amazing place to just to visit, forget the shopping!